[Lapack] [lapackers] bug in DGEHRD

From: James Demmel
Date: Wed, 21 Apr 2010 18:17:13 -0700

The balancing is choosing to scale some rows/columns by factors like 1e18,
which rather amplifies tiny rounding errors in the (presumably correctly)
computed eigenvectors of the balanced matrix, when balancing is undone
at the end.
The expert driver interface dgeevx would let the user disable balancing,
until
we figure out whether this is a bug or a feature, I'm not sure which.
Jim
Julien Langou wrote:

We have a bug report at:
http://icl.cs.utk.edu/lapack-forum/viewtopic.php?f=2&t=1818
It comes from Numpy guys.
The matrix is very pretty to look at with a lots of zero and a lots of
structure but DGEHRD does not seem to like, not one little bit. See post.
Note that while
[V,D]=eig(A);
does not work,
[Q,H]=hess(A);
[V,D]=eig(H);
V = Q*V;
works ...
Ideas?
Best wishes,
Julien.